Yes, this is exactly right. You become more aware of outside stimula,
because you realize that you are really in bed asleep, and you tend to start
trying to see and feel the real world instead of the dream.

The spinning idea was published in Discover magazine, and they said they
didn't know why it worked. I don't think that balance has anything to do
with it. With many years of experience, I have my own theory. I believe
that when you start spinning, your field of vision moves around to see new
things that were outside of your field of view before. Your
dream-generating parts of your mind have to go into full dream-production
mode to generate the new field of view. This strengthens the dream, and
also gives you more dream stimulus to interpret, so you are less likely to
detect the real world stimulus.

The only thing that makes sense about the balance is that you don't want
your internal sense of balance to realize that you are lying down. You want
to dream that you are standing up (usually). Spinning might confuse this
sense to be unsure which way is down, and which way you are lying down. I
still prefer my first theory above.